 | Euclid, James Thomson - 1845 - 382 σελίδες
...to DFE, and A to D. Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. — If two triangles have one angle...the sides about the equal angles proportionals; the remaining angles are equal, each to each, viz. those which are opposite to the homologous sides. Let... | |
 | Euclid - 1845 - 218 σελίδες
...ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — If two triangles have one angle of the one equal to one angle of the oiher, and the sides about the equal angles proportionals, the triangles shall be equiangular, and... | |
 | Scottish school-book assoc - 1845 - 444 σελίδες
...halves of parallelograms, upon the same base, and having the same altitude, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about these angles reciprocally proportional ; and if two triangles have one angle of... | |
 | Euclides - 1845 - 546 σελίδες
...AB, BC, a mean proportional -DB is found. QEF ^ PROPOSITION XIV. THEOREM. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and conversely, parallelograms... | |
 | Euclides - 1846 - 272 σελίδες
...therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which have one angle of the one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3.... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...the parallelogram AB is equal (9. 5.) to the parallelogram BC. PROP. XV. THEOR. Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional ; And triangles which have one angle... | |
 | Euclides - 1846 - 292 σελίδες
...parallelogram BC. Wherefore, Equal parallelograms *rc. QED PROP. XV. THEOR. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and triangles, which have one angle... | |
 | Dennis M'Curdy - 1846 - 168 σελίδες
...of two triangles, &c. QED Kecite (a) p. 23, 1; Wp.9,5; (4) 32, 1 ; (Op.8,1: p. 4, 6; ax. 1,1. 6 Th. If two triangles have one angle of the one equal to one of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,... | |
 | Harvey Goodwin (bp. of Carlisle.) - 1847 - 136 σελίδες
...than the sum of the two sides by the diameter of the inscribed circle. 23. If two triangles have an angle of the one equal to one angle of the other, and also another angle of the one equal to the supplement of another angle of the other, the sides about... | |
 | Bengal council of educ - 1848 - 394 σελίδες
...definition will satisfy one of the tests of the former. 2. Give a proof of the following proposition : " If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then, if each of the remaining angles be either less, or not less... | |
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If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. 
